Question

factorise the following:-



plz don't spam_/!\_


otherwise strictly report!!-_-​

Answer 1

x^4 + 4

Adding and subtracting 4x^2, we get

x^4+ 4x^2- 4x^2+ 4

= (x^2 + 2)^2. - (2x)^2

= (x^2 + 2x + 2)(x^2 - 2x + 2)

As a^2 - b^2 = (a+b)(a-b)

hope helpful :-)

Answer 2

To Factorise:

x⁴ + 4

Solution:

$\sf{x^4 + 4}$

$\sf{\implies(x^2 + 2)^2 -2(x^2)(2)\:\:\: [ ∵ (a + b)^2 = a^2 + b^2 + 2ab]}$

$\implies\sf{(x^2 + 2)^2 - 4x^2}$

${\boxed{\sf{\red{here, a = x^2, b = 2}}}}$

$\sf{\implies(x^2 +2)^2 - (2x)^2 \:\:\: [ ∵ (a^2 - b^2 = (a + b)(a - b)]}$

$\implies\sf{( x^2 + 2 + 2x)(x^2 + 2 - 2x)}$

$\implies\sf\underline\purple{(x^2 + 2x + 2)(x^2 - 2x + 2)}$

☆ $\sf\underbrace\color{green}{more\: information}$ ☆

$\rightarrow\sf{ (a + b)^2 = a^2 + b^2 + 2ab}$

$\rightarrow\sf{(a - b)^2 = a^2 + b^2 - 2ab}$

$\rightarrow\sf{a^2 - b^2 = (a + b)(a - b)}$

$\rightarrow\sf{ a^2 + b^2 = (a + b)^2 - 2ab}$

$\rightarrow\sf{2(a^2 + b^2) = (a + b)^2 + (a - b)^2}$